A recent theorem of Bissacot, et al. proved using results about the cluster expansion in statistical mechanics extends the Lovász Local Lemma by weakening the conditions under which its conclusions holds. In this note, we prove an algorithmic analog of this result, extending Moser and Tardos's recent algorithmic Local Lemma, and providing an alternative proof of the theorem of Bissacot, et al. applicable in the Moser-Tardos algorithmic framework.